Simplify the following expression: $k = \dfrac{-2n^2 + 8n + 24}{n - 6} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ k =\dfrac{-2(n^2 - 4n - 12)}{n - 6} $ Then we factor the remaining polynomial: $n^2 {-4}n {-12} $ ${-6} + {2} = {-4}$ ${-6} \times {2} = {-12}$ $ (n {-6}) (n + {2}) $ This gives us a factored expression: $\dfrac{-2(n {-6}) (n + {2})}{n - 6}$ We can divide the numerator and denominator by $(n + 6)$ on condition that $n \neq 6$ Therefore $k = -2(n + 2); n \neq 6$